Using a geometric sequence, it is found that 7 rounds must be scheduled in order to complete the tournament.
<h3>What is a geometric sequence?</h3>
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
![a_n = a_1q^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20a_1q%5E%7Bn-1%7D)
In which
is the first term.
In this problem, the first round has 128 players, and each round, the players who lose a game go home, hence the common ratio is of q = 0.5.
Then, the geometric sequence for the number of players after n rounds is given by:
![a_n = 128(0.5)^n](https://tex.z-dn.net/?f=a_n%20%3D%20128%280.5%29%5En)
In the final round, there is one player, hence:
![1 = 128(0.5)^n](https://tex.z-dn.net/?f=1%20%3D%20128%280.5%29%5En)
![(0.5)^n = \frac{1}{128}](https://tex.z-dn.net/?f=%280.5%29%5En%20%3D%20%5Cfrac%7B1%7D%7B128%7D)
![(0.5)^n = \left(\frac{1}{2}\right)^7](https://tex.z-dn.net/?f=%280.5%29%5En%20%3D%20%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E7)
n = 7
7 rounds must be scheduled in order to complete the tournament.
More can be learned about geometric sequences at brainly.com/question/11847927
#SPJ1